This invention relates to a method of determining a given characteristic of a material sample such as a semiconductor material sample. In particular, but not exclusively, this invention relates to a method of determining a given characteristic, such as the strain profile of an ion implanted sample or the thicknesses or lattice mismatch between layers of a multi-layer sample using X-ray analysis techniques.
Often much information about a material sample can in principle be obtained from a profile of a given characteristic obtained by making measurements on the sample. However, in practice it can be very difficult to extract that information by making measurements directly on the experimental profile and it may be possible to extract more information by comparing the experimental profile with a calculated profile and adjusting the parameters used to obtain the calculated profile until a fit is achieved. This can prove a difficult process, especially if the experimental profile is complex and contains many peaks and troughs representing structural information.
Analysis of diffraction patterns using a probe beam such as an X-ray radiation beam has been widely used to investigate material samples, for example natural crystals and manufactured multi-layer material samples. In such analysis, an apparatus generally known as a diffractometer is used to obtain a diffraction profile by rotating a material sample relative to an incident probe beam and detecting the intensity of the beam diffracted by the sample at each angle of rotation to obtain a spectrum or profile relating the intensity of the diffracted beam to the angle of the sample. The probe beam need not necessarily be an X-ray beam but could be, for example, a gamma (g) ray radiation beam, an ultra violet radiation beam or an infra red beam or a particle beam such as a beam of neutrons or electrons. For a general explanation of X-ray analysis techniques reference may be made to many textbooks, for example "b X-ray diffraction procedures" by H. P. Klug and L. E. Alexander published by John Wiley & Sons.
Generally, such X-ray diffraction profiles are complex and structural information cannot be accurately obtained simply from the experimental profile because the data represents only the intensity and not the phase of the diffracted signal and phase information is generally necessary to obtain structural information about a sample, especially if the sample is itself complex. This is explained for the case of a multilayer sample in a paper entitled "Composition and lattice mismatch measurement of thin semiconductor samples by X-ray diffraction" by P. F. Fewster and C. J. Curling published in the Journal of Applied Physics 62 (10), Nov. 15, 1987 at pages 4154 to 4158.
In the light of these problems, the approach generally adopted is to calculate a likely diffraction profile by postulating a tidal structure for the sample using, for example, information obtained from the sample preparation process, and then to compare the calculated diffraction profile with the experimental diffraction profile and to adjust the parameters determining the calculated diffraction profile by trial and error so as to refine the calculated diffraction profile until an acceptable fit is achieved between the calculated and experimental diffraction profiles, thereby indicating that the same parameters fit the experimental and the calculated diffraction profiles.
Such a procedure is extremely time-consuming and very dependent on the accuracy of the initial "guess" at the sample structure used to obtain the calculated profile which in turn is dependent on the amount and accuracy of information available about the sample structure from, for example, the sample preparation or growth process.
In addition, generally a high resolution diffraction profile such as an X-ray diffraction profile contains a wealth of information and is sensitive to many parameters which can lead to correlations between parameters and false minima making most fitting procedures (for example a least squares approach) very difficult and possibly leading to an incorrect result or more likely to an increase in the computation time required to achieve an acceptable result.
In view of the above-mentioned problems, particularly that of postulating an accurate structure from which the initial trial calculated profile is obtained, the formulation of an expert system has been proposed by T. Tjahjadi and D. K. Brown in a paper entitled "an expert system for X-ray diffraction profile analysis" presented at the International Conference '89 on "Expert Systems in Engineering Applications" held in Wuhan, China from 12th to 17th Oct., 1989 and published in the proceedings of that Conference by Huazhong University of Science and Technology Press. Although an expert system approach may well lead to improved results it requires a large amount of expenditure in time and computing power to set up an acceptable system. In addition, an expert system necessarily requires an expert knowledge base and will only be as useful or accurate as the information contained within that knowledge base. Naturally, such an expert system will only be ably to cope with problem for which it has been designed.
It is an aim of the present invention to provide a method of determining a given characteristic of a material sample which mitigates the problems mentioned above.